Identification of diffusion parameters in a non-linear convection–diffusion equation using adaptive homotopy perturbation method

This paper is concerned with the numerical identification of diffusion parameters in a non-linear convection–diffusion equation, which arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. In order to overcome the defect of the local convergence of traditional methods, an adaptive homotopy perturbation method is applied to solve this parameter identification inverse problem. The adaptive homotopy perturbation method provides a simple way to adapt computational refinement to the choice of the homotopy parameter. Numerical simulations illustrate that the proposed algorithm is globally convergent and computationallyefficient.     

FUZZIFYING THE “PRECISE”

Based on the fuzzy-integral model, methods and algorithms are developed for identifying the “input–output” operator of continuous and stationary discrete extremal fuzzy dynamic systems (EFDS). The EFDS “input–output” operator is restored by means of experimental data with possibilistic uncertainty, the source of which is extremal fuzzy time intervals. The regularization conditions for obtaining quasi-optimal estimates are substantiated by the proved theorems. The corresponding algorithms are provided. The results obtained are illustrated by examples in the case of a finite set of EFDS states.     

Mixed norm regularized recursive total least squares for group sparse system identification

A mixed l_p,0‐regularized recursive total least squares (RTLS) algorithm is considered for group sparse system identification. Regularized recursive least squares (RLS) has been successfully applied to group sparse system identification; however, the estimation performance in regularized RLS‐based algorithms deteriorates when both input and output are contaminated by noise (the error‐in‐variables problem). We propose an l_p,0‐RTLS algorithm to handle group sparse system identification with errors‐in‐variables. The proposed algorithm is an RLS‐like solution that utilizes l_p,0‐regularization. The proposed algorithm provides excellent performance as well as reduces the required complexity by effective inversion matrix handling. Simulations demonstrate the superiority of the proposed l_p,0‐regularized RTLS for a group sparse system identification setting. Copyright © 2015 John Wiley & Sons, Ltd.     

Image denoising via sparse coding using eigenvectors of graph Laplacian

Image denoising plays an important role in image processing, which aims to separate clean images from the noisy images. A number of methods have been presented to deal with this practical problem in the past decades. In this paper, a sparse coding algorithm using eigenvectors of the graph Laplacian (EGL-SC) is proposed for image denoising by considering the global structures of images. To exploit the geometry attributes of images, the eigenvectors of the graph Laplacian, which are derived from the graph of noised patches, are incorporated in the sparse model as a set of basis functions. Sequently, the corresponding sparse coding problem is presented and efficiently solved with a relaxed iterative method in the framework of the double sparsity model. Meanwhile, as the denoising performance of the EGL-SC significantly depends on the number of the used eigenvectors, an optimal strategy for the number selection is employed. A parameter called as out-of-control rate is set to record the percentage of the denoised patches that suffer from serious residual errors in the sparse coding procedure. Thus, with the eigenvector number increasing, the appropriate number can be heuristically selected when the out-of-control rate falls below an empirical threshold. Experiments illustrate that the EGL-SC can achieve a better performance than some other well-developed denoising methods, especially in the structural similarity index for the noise of large deviations.     

脉冲风洞短时测力信号的延拓与动态载荷辨识方法

研究了一种可快速辨识脉冲风洞中试验模型所受动态载荷的方法。给出了载荷、系统单位脉冲响应函数、天平输出三者的时域离散化模型,指出后者是前两者线性卷积的截断;将天平短时振荡输出延拓为完整的线性卷积结果,对前两者补零延拓,将上述模型转化为圆周卷积形式,进而通过离散傅里叶变换得到三者的频域离散化模型,求解频域模型得到载荷。通过单自由度系统简单载荷、多自由度系统复杂载荷两个数值模拟算例验证了该方法仅需对测量信号低通滤波即可准确辨识出载荷;经风洞试验,验证了方法的准确性和实用性。     

基于变分正则化的低质视频图像二维增强仿真

受环境、硬件设备及成本等因素限制,所生产的视频质量低,存在大量冗余噪声,导致局部区域图像模糊不清,无法对目标个体判定或识别。为解决上述问题,构建一种基于变分正则化的低质视频图像二维增强方法。通过采集先验信息,确定噪声去除和质量增强区域,随后使用ROF经典模型和偏微分对原始图像做平滑及去噪处理,并提出前后扩散方程,使方法能够有效抑制背景区域噪声,并对目标个体边缘做锐化处理,利用变分正则化提升视频图像整体分辨率,使其完成图像二维增强。仿真结果表明,所提方法具有控制噪声与加强图像质量双重优势,有效去除、抑制噪声影响,提升目标个体区域强散射点,且方法复杂程度较低,能够实现低质视频图像的均衡优化。     

正则化图形模糊聚类及鲁棒分割算法

针对现有图形模糊聚类算法合理性差和抗噪能力弱的问题，提出嵌入对称正则项的图形模糊聚类鲁棒算法。将样本聚类所对应的中立度与拒分度相结合构造对称正则项，嵌入现有图形模糊聚类所对应的目标函数；同时，利用像素邻域所对应的均值信息辅助当前像素聚类并构造了空间信息约束正则项，采用拉格朗日乘子法获得正则化图形模糊聚类鲁棒分割算法。不同噪声干扰图像分割结果表明，所建议的分割算法是有效的，相比现有的鲁棒模糊聚类分割算法具有更强的抑制噪声能力。     

A Gaussian RBFs method with regularization for the numerical solution of inverse heat conduction problems

In this paper, a recursion numerical technique is considered to solve the inverse heat conduction problems, with an unknown time-dependent heat source and the Neumann boundary conditions. The numerical solutions of the heat diffusion equations are constructed using the Gaussian radial basis functions. The details of algorithms in the one-dimensional and two-dimensional cases, involving the global or partial initial conditions, are proposed, respectively. The Tikhonov regularization method, with the generalized cross-validation criterion, is used to obtain more stable numerical results, since the linear systems are badly ill-conditioned. Moreover, we propose some results of the condition number estimates to a class of positive define matrices constructed by the Gaussian radial basis functions. Some numerical experiments are given to show that the presented schemes are favourably accurate and effective.     

An adaptive Tikhonov regularization parameter choice method for electrical resistance tomography

Electrical resistance tomography (ERT) reconstructs the conductivity distribution from the boundary changes of electrical measurements. The inverse problem of ERT is seriously ill-posed where regularization methods are needed to treat this ill-posedness. A proper choice of regularization parameter which controls the degree of smoothing is very important for these regularization methods. Although have been a variety of methods, such as L-curve method, to choose a reasonable parameter for the problem, these methods usually result in a scalar parameter which cannot distinctly express the spatial characteristic of the conductivity distribution. So a spatially adaptive regularization parameter choice method is proposed for regularizing the inverse problem of ERT based on Tikhonov regularization. Since large regularization parameters can stabilize and smoothen the solution, while small regularization parameters can approximate and sharpen the solution, the proposed method adaptively updates the regularization parameters during the iteration process and provides spatially varying parameter for each pixel of the reconstructed image. When the iteration is stopped, large regularization parameters for the smooth background region and small regularization parameters for the object region can be obtained. The method is discussed using simulated data for some typical conductivity distributions, and further applied to the analysis of real measurement data acquiring from the practical system. The results demonstrate that flexible regularization parameter vectors can be achieved for different distributions and the strength of regularization is adaptively provided for different regions in a specific distribution. The adaptive method achieves an efficient and reliable regularization solution and has outstanding performance in noise immunity especially in smooth background regions.     

Gaussian-Hermite moment-based depth estimation from single still image for stereo vision

Depth information of objects plays a significant role in image-based rendering. Traditional depth estimation techniques use different visual cues including the disparity, motion, geometry, and defocus of objects. This paper presents a novel approach of focus cue-based depth estimation for still images using the Gaussian-Hermite moments (GHMs) of local neighboring pixels. The GHMs are chosen due to their superior reconstruction ability and invariance properties to intensity and geometric distortions of objects as compared to other moments. Since depths of local neighboring pixels are significantly correlated, the Laplacian matting is employed to obtain final depth map from the moment-based focus map. Experiments are conducted on images of indoor and outdoor scenes having objects with varying natures of resolution, edge, occlusion, and blur contents. Experimental results reveal that the depth estimated from GHMs can provide anaglyph images with stereo quality better than that provided by existing methods using traditional visual cues.